Hilbert series and obstructions to asymptotic semistability
type: Item
instance of: scholarly article
title: Hilbert series and obstructions to asymptotic semistability
zbMATH Open document ID: 1209.53059
author: Akito Futaki
author: Hajime Ono
author: Yuji Sano
published in: Advances in Mathematics
publication date: 2010-12-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/0811.1315
review text: The first part of the survey deals with problems related to integral invariants for toric Fano manifolds. The second part deals with the definition of asymptotic Chow semistability. The basic results are given. In the third part is given the main result of this paper which claims that: ``Given a polarized manifold there are obstructions for asymptotic Chow semistability described as integral invariants which can be regarded as characters of the Lie algebra of holomorphic vector fields. In this paper we show that, on toric Fano manifolds the linear span of those Lie algebra characters coincides with the derivatives of the Laurent series of the Hilbert series.'' In sections 4,5 and 6 are also considered other problems. In the final section 7 the authors discusse the possible extension to general compact Sasaki manifolds. The bibliography contains 38 references. In summary this is an excellent paper.
reviewed by: Petre Stavre
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 5825410
zbMATH Keywords: asymptotic semistability
zbMATH Keywords: Kähler metric of constant scalar curvature
zbMATH Keywords: toric Fano manifold
MaRDI profile type: Publication
OpenAlex ID: W2064101548
arXiv ID: 0811.1315
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DOI: 10.1016/J.AIM.2010.06.018
description: scientific article